Number Theory

Explore the powers of divisibility, modular arithmetic, and infinity.

Last Digits

Secret Messages

Rainbow Cycles

Divisibility Shortcuts

More Divisibility Shortcuts

Divisibility by 9 and 3

Last Digits

Arithmetic with Remainders

Digital Roots

Factor Trees

Prime Factorization

Factoring Factorials

Counting Divisors

100 Doors

How Many Prime Numbers Are There?

100 Doors Revisited


Billiard Tables


Dots on the Diagonal

Number Jumping (I)

Number Jumping (II)

Number Jumping (III)

Relating LCM and GCD

Billiard Tables Revisited (I)

Billiard Tables Revisited (II)

Times and Dates

Modular Congruence

Modular Arithmetic

Divisibility by 11

Star Drawing (I)

Star Drawing (II)

Star Drawing (III)

Die-Hard Decanting (I)

Die-Hard Decanting (II)

Additive Cycles

Modular Multiplicative Inverses

Multiplicative Cycles

Fermat's Little Theorem


Last Digits Revisited

Perfect Shuffling

Counting to Infinity

Multiple Infinities

Hilbert's Hotel

Infinitely Large

Course description

This course starts at the very beginning — covering all of the essential tools and concepts in number theory, and then applying them to computational art, cryptography (code-breaking), challenging logic puzzles, understanding infinity, and more!

Topics covered

  • Divisibility Shortcuts
  • Exploring Infinity
  • Factor Trees
  • Fermat's Little Theorem
  • Greatest Common Divisor
  • Least Common Multiple
  • Modular Arithmetic
  • Modular Congruence
  • Modular Inverses
  • Prime Factorization
  • The 100 Doors Puzzle
  • Totients

Prerequisites and next steps

A basic understanding of exponents and multiplication is all you need!


  • Mathematical Fundamentals

Next steps